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1. $\frac{12}{13}$

Answer: Option D

Explanation:

\cot A = \frac{\cos A}{\sin A} = \pm \sqrt{\frac{1 - \sin^{2} A}{\sin A}} = \pm \frac{\sqrt{{(\frac{12}{13})}^{2}}}{\frac{12}{13}} = \pm \frac{\sqrt{1 - \frac{144}{169}}}{\frac{12}{13}} = \pm \frac{\frac{\sqrt{169 - 144}}{169}}{\frac{12}{13}} = \pm \frac{\sqrt{\frac{25}{169}}}{\frac{12}{13}} = \pm \frac{\frac{5}{13}}{\frac{12}{13}} = \pm \frac{5}{13} \times \frac{13}{12} = \pm \frac{5}{12}

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